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- W2414909849 abstract "We study the communication rate of coding schemes for interactive communication that transform any two-party interactive protocol into a protocol that is robust to noise. Recently, Haeupler (FOCS '14) showed that if an $epsilon > 0$ fraction of transmissions are corrupted, adversarially or randomly, then it is possible to achieve a communication rate of $1 - widetilde{O}(sqrt{epsilon})$. Furthermore, Haeupler conjectured that this rate is optimal for general input protocols. This stands in contrast to the classical setting of one-way communication in which error-correcting codes are known to achieve an optimal communication rate of $1 - Theta(H(epsilon)) = 1 - widetilde{Theta}(epsilon)$. In this work, we show that the quadratically smaller rate loss of the one-way setting can also be achieved in interactive coding schemes for a very natural class of input protocols. We introduce the notion of average message length, or the average number of bits a party sends before receiving a reply, as a natural parameter for measuring the level of interactivity in a protocol. Moreover, we show that any protocol with average message length $ell = Omega(mathrm{poly}(1/epsilon))$ can be simulated by a protocol with optimal communication rate $1 - Theta(H(epsilon))$ over an oblivious adversarial channel with error fraction $epsilon$. Furthermore, under the additional assumption of access to public shared randomness, the optimal communication rate is achieved ratelessly, i.e., the communication rate adapts automatically to the actual error rate $epsilon$ without having to specify it in advance. This shows that the capacity gap between one-way and interactive communication can be bridged even for very small (constant in $epsilon$) average message lengths, which are likely to be found in many applications." @default.
- W2414909849 created "2016-06-24" @default.
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- W2414909849 date "2017-01-01" @default.
- W2414909849 modified "2023-09-27" @default.
- W2414909849 title "Bridging the Capacity Gap Between Interactive and One-Way Communication" @default.
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- W2414909849 doi "https://doi.org/10.1137/1.9781611974782.138" @default.
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